The navy blamed the killings on a drugs gang known as the New Generation, which is involved in a battle for territory with the rival Zetas cartel.
At least 12 suspected members of the Zetas have also been arrested.
New Generation gang members also call themselves the "Matazetas" or "Zetas-killers" because of their feud with the rival group.
Videos posted on the internet in recent months showed masked gunmen promising to free Veracruz from kidnapping, murder and extortion by the Zetas.
Presidential tweet But the navy dismissed suggestions that they were dealing with a paramilitary group that had been set up to combat the cartel.
"We stress that this is just another organised crime gang that opposes the Zetas, with whom they are fighting for control of illicit incomes," navy spokesman Jose Luis Vergara said.
"No criminal act or propaganda will make the state withdraw," he added.
The 20 detainees were paraded in front of the media at a navy air base in Mexico City.
Mexican President Felipe Calderon welcomed the arrests.
"The violence in Veracruz is lamentable. But the navy has delivered a major blow by capturing members of the Zetas and Zetas-killers," he wrote on Twitter.
The Mexican security forces have been under growing pressure to show results in the fight against organised crime in Veracruz state, which has seen an upsurge in drug-related violence in recent months.
The 32 bodies were found just days after the government unveiled a plan to boost security in Veracruz.
The New Generation cartel is thought to be linked to the Sinaloa cartel led by Joaquin Guzman - Mexico's most-wanted drugs lord.
The Sinaloa cartel is involved in a bloody fight with Zetas for control of territory and drug-trafficking routes to the US.
An estimated 40,000 people have been killed in drug-related violence in Mexico since 2006, when President Calderon began deploying troops to fight the drugs gangs.
The Mexican Navy has played a key role in that offensive, capturing or killing some of the most wanted drugs suspects.